Answer:
1.8732, 0.068
Step-by-step explanation:
Given that according to the National Association of Realtors, it took an average of three weeks to sell a home in 2017.
Sample size n = 39
a)
Std error of sample =
(Two tailed test at 5% significance level)
Mean difference = 0.6
Since population std deviation is not known, t test to be used.
b) Test statistic t = mean diff/std error =
df = 38
c) p value = 0.068
Answer:
The whole numbers are 0 and 79.
Step-by-step explanation:
The numbers provided are as follows:
Whole numbers are a set of natural positive numbers and 0. This set basically consists of counting discrete numbers.
Such as: 0, 1, 2, 3, 4, 5....
From the provided set of numbers the whole numbers are:
S = {79 and 0}
Thus, the whole numbers are 0 and 79.
Answer:
Step-by-step explanation:
Hello!
Given the variables
X: Curfew of middle school students (Categorized Yes/No)
Y: Average grade of middle school students. (Categorized: A, B, C, and D)
The objective is to test if there is an association between both variables, you have to conduct a Chi-Square test of independence.
In the null hypothesis, you state that both variables are independent vs. the alternative hypothesis that the variables are dependent.
The hypotheses for this test are:
H₀: Pij= Pi. * P.j i= (1)Yes, (2)No; j= (1)A, (2)B, (3)C, (4)D
H₁: Te variables are not independent.
α: 0.05
Where
Oij is the observed frequency for the i-row and j-column
Eij is the expected frequency for the i-row and j-column
r= number of categories in the rows
c= number of categories in the columns
p-value: 0.687
The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. So using a 5% significance level, you can conclude that having a curfew and the average grades of middle schoolers are two independent variables.
Answer:
Maximum Area of the basketball court = 1250 ft²
Maximum area of the playground = 400 ft²
The basketball is 3.125 times larger than than the playground.
Step-by-step explanation:
The diagram representing the description is attached to this solution.
The big rectangle represents the basketball court.
The small rectangle represents the playground.
Let the length and width of the basketball court be y and x respectively.
The length and width of the small playground will be (y-30) and (x-5) respectively
The Area of the basketball court is
A(x, y) = xy
But, 2x + y = 100
We can maximize the Area by turning the two variable function into a one variable function and substituting for y in the Area equation.
2x + y = 100
y = 100 - 2x
A(x, y) = xy
A(x) = x(100 - 2x) = 100x - 2x²
A(x) = 100x - 2x²
At maximum point, (dA/dx) = 0 and (d²A/dx²) < 0, that is, negative.
(dA/dx) = 100 - 4x = 0
(d²A/dx²) = -4 < 0
Hence, it's a maximum point.
At maximum point,
(dA/dx) = 100 - 4x = 0
100 - 4x = 0
4x = 100
x = 25 ft
y = 100 - 2x = 100 - 2(25) = 100 - 50 = 50 ft
Hence, the length and width of the basketball court that maximizes the Area are 50 ft and 25 ft respectively.
For the small playground,
The length = (y - 30) = (50 - 30) = 20 ft
The width = (x - 5) = (25 - 5) = 20 ft
Maximum Area of the basketball court = xy = (50)(25) = 1250 ft²
Maximum area of the playground = (y-30)(x-5) = (20)(20) = 400 ft²
Ratio of the Areas = (1250/400) = 3.125
The basketball is 3.125 times larger than than the playground
Hope this Helps!!!
